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Electronic Colloquium on Computational Complexity

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REPORTS > KEYWORD > CHROMATIC NUMBER:
Reports tagged with Chromatic Number:
TR95-024 | 23rd May 1995
Mihir Bellare, Oded Goldreich, Madhu Sudan

Free bits, PCP and Non-Approximability - Towards tight results

Revisions: 4

This paper continues the investigation of the connection between proof
systems and approximation. The emphasis is on proving ``tight''
non-approximability results via consideration of measures like the
``free bit complexity'' and the ``amortized free bit complexity'' of
proof systems.

The first part of the paper presents a collection of new ... more >>>


TR00-062 | 25th August 2000
Venkatesan Guruswami, Johan Hastad, Madhu Sudan

Hardness of approximate hypergraph coloring

We introduce the notion of covering complexity of a probabilistic
verifier. The covering complexity of a verifier on a given input is
the minimum number of proofs needed to ``satisfy'' the verifier on
every random string, i.e., on every random string, at least one of the
given proofs must be ... more >>>


TR00-073 | 28th August 2000
Venkatesan Guruswami, Sanjeev Khanna

On the Hardness of 4-coloring a 3-colorable Graph

We give a new proof showing that it is NP-hard to color a 3-colorable
graph using just four colors. This result is already known (Khanna,
Linial, Safra 1992), but our proof is novel as it does not rely on
the PCP theorem, while the earlier one does. This ... more >>>


TR05-100 | 30th August 2005
David Zuckerman

Linear Degree Extractors and the Inapproximability of Max Clique and Chromatic Number

A randomness extractor is an algorithm which extracts randomness from a low-quality random source, using some additional truly random bits. We construct new extractors which require only log n + O(1) additional random bits for sources with constant entropy rate. We further construct dispersers, which are similar to one-sided extractors, ... more >>>


TR16-029 | 7th March 2016
Joshua Brakensiek, Venkatesan Guruswami

New hardness results for graph and hypergraph colorings

Finding a proper coloring of a $t$-colorable graph $G$ with $t$ colors is a classic NP-hard problem when $t\ge 3$. In this work, we investigate the approximate coloring problem in which the objective is to find a proper $c$-coloring of $G$ where $c \ge t$. We show that for all ... more >>>




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